How do I override, not hide, a member variable (field) in a C# subclass?

You cannot override variables in C#, but you can override properties:

public class Item
{
    public virtual string Name {get; protected set;}
}
public class Subitem : Item
{
    public override string Name {get; protected set;}
}

Another approach would be to change the value in the subclass, like this:

public class Item
{
    public string Name = "Item";
}
public class Subitem : Item
{
    public Subitem()
    {
        Name = "Subitem";
    }
}